Abstract:
Cytoskeletal motors known as motor proteins are molecules that drive cellular transport along
several parallel cytoskeletal filaments and support many biological processes. Experimental evidence
suggests that they interact with the nearest molecules of their filament while performing any mechanical
work. To understand such mechanism theoretically, a new version of two-channel totally
asymmetric simple exclusion process which incorporates interactions in a thermodynamically consistent
way is introduced. As the existing approaches for multi-channel systems deviate from analyzing
the combined effect of inter and intra-channel interactions, a new approach known as modified vertical
cluster mean field is developed. The approach along with monte-carlo simulations successfully
encounters some correlations and computes the complex dynamic properties of the system. Role
of symmetry of interactions and inter-channel coupling is observed on the triple points and the
particle maximal current. Surprisingly, for all values of coupling rate and most of the interaction
splittings, the optimal interaction strength corresponding to maximal current belongs to the case of
weak repulsive interactions. Moreover, for weak interaction splittings and with an increase in the
coupling rate, the optimal interaction strength tends towards the known experimental results. Coupling
in between the lanes decreases the correlations. They are found to be short-range and weaker
for repulsive and weak attractive interactions, while long-range and stronger for large attractions.
